The seminar is joint for the division of Analysis and Probability and its main themes are Mathematical Physics, Probability Theory and Harmonic and Functional Analysis. The seminar is encouraged to be aimed at a broader audience, but it may be of a more specialised nature when indicated in the last line of the abstract.
The talks in the seminar are usually 60 minutes, but can also be in the format 2x45 minutes when indicated in the abstract.
The seminar takes place Tuesdays at 1315-1415 in MV:L15 unless otherwise indicated.
Should you have any questions or suggestions, feel free to email one of the organizers Martin Hallnäs (Mathematical Physics), Erik Broman (Probability Theory) or Magnus Goffeng (Harmonic and Functional Analysis).
2020-01-28 (N.B. MVL14)
Peter Sjögren (Chalmers/GU)
Sharp estimates for the heat kernel in compact rank-one symmetric spaces
We prove sharp two-sided estimates for the heat kernel in any compact Riemannian symmetric space of rank one. As examples of such spaces, we will consider the real and the complex hyperbolic spaces. When the arguments of this heat kernel consists of two almost antipodal points, the kernel has a special behaviour. This phenomenon was found earlier by the authors in the case of the Euclidean sphere. We give similar estimates for heat kernels in the unit ball and for those associated with classical Jacobi expansions. The Jacobi case is the key to the proofs of the results.
This is joint work with A. Nowak and T.Z. Szarek, Wroclaw.
No knowledge of symmetric spaces is required to follow the talk, but it is good to know roughly what a Riemannian manifold is.